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arxiv: 2604.05862 · v1 · submitted 2026-04-07 · 💻 cs.DC

Recognition: 2 theorem links

· Lean Theorem

Communication Requirements for Linearizable Registers

Ra\"issa Nataf , Yoram Moses
Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:35 UTC · model grok-4.3

classification 💻 cs.DC
keywords linearizabilityatomic registersasynchronous systemsmessage passingcommunication requirementsmessage chainsreal-time orderingdistributed computing
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The pith

Linearizable register implementations in asynchronous message-passing systems must create extensive message chains among operations of all types.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that linearizable atomic registers require long chains of messages connecting reads and writes to preserve real-time ordering. In asynchronous systems the only available ordering signal is that a send precedes a receive, so without such chains an adversary can delay or reorder operations without any process detecting the change. A reader cares because this shows why linearizable implementations are necessarily communication-heavy and structurally nontrivial even for the simplest shared object.

Core claim

Linearizable implementations of atomic registers must create extensive message chains among operations of all types. Two general theorems establish that message chains are required to prevent undetectable delays and reorderings of actions; because linearizability demands that real-time order be respected and async systems supply only send-before-receive causality, the chains become mandatory.

What carries the argument

Message chains that link the send and receive events of operations, thereby enforcing the real-time precedence required by linearizability when no clocks are present.

If this is right

  • Linearizable register implementations are necessarily costly in communication.
  • All operation types, including reads and writes, must participate in the required message chains.
  • No trivial or minimal-message implementation can satisfy linearizability in async settings.
  • The structure of any correct implementation is constrained by the need to propagate ordering information via chains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same chain requirement is likely to appear for other linearizable objects such as queues or counters.
  • Designers may trade off linearizability for weaker models precisely to avoid these communication costs.
  • Adding even weak timing assumptions or oracles could reduce the necessary chain length.

Load-bearing premise

The system is fully asynchronous, so the only ordering information available is that sending a message precedes its delivery.

What would settle it

An implementation of a linearizable register in a fully asynchronous message-passing system that uses only a bounded number of messages and creates no chains linking distinct operations.

read the original abstract

While linearizability is a fundamental correctness condition for distributed systems, ensuring the linearizability of implementations can be quite complex. An essential aspect of linearizable implementations of concurrent objects is the need to preserve the real-time order of operations. In many settings, however, processes cannot determine the precise timing and relative real-time ordering of operations. Indeed, in an asynchronous system, the only ordering information available to them is based on the fact that sending a message precedes its delivery. We show that as a result, message chains must be used extensively to ensure linearizability. This paper studies the communication requirements of linearizable implementations of atomic registers in asynchronous message passing systems. We start by proving two general theorems that relate message chains to the ability to delay and reorder actions and operations in an execution of an asynchronous system, without the changes being noticeable to the processes. These are then used to prove that linearizable register implementations must create extensive message chains among operations of \emph{all} types. In particular, our results imply that linearizable implementations in asynchronous systems are necessarily costly and nontrivial, and provide insight into their structure.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper proves two general theorems relating the existence of message chains in asynchronous message-passing executions to the indistinguishability of executions under reordering and delaying of actions. These theorems are instantiated for atomic registers to establish that any linearizable implementation must induce extensive message chains among operations of all types (reads and writes), implying that linearizable register implementations in asynchronous systems are necessarily costly and nontrivial.

Significance. If the central claim holds, the result provides a fundamental structural insight into the communication requirements of linearizability, showing that real-time order preservation forces chains linking all operation types. The general theorems are a strength: they are derived directly from the asynchronous model without hidden progress assumptions or fitted parameters, and their application to registers is direct with no gaps in the mapping from semantics to reordering conditions.

minor comments (2)
  1. The abstract and introduction use the term 'extensive' in italics without an immediate formal definition; a brief inline characterization (e.g., chains connecting every pair of operation types) would improve readability before the theorems are stated.
  2. The two general theorems are described as relating message chains to indistinguishability, but the manuscript would benefit from an explicit statement of the model assumptions (e.g., reliable channels, no process failures) at the start of §3 to make the scope of the theorems immediately clear.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the paper and for recommending acceptance. We are pleased that the referee recognizes the value of the general theorems relating message chains to indistinguishability under reordering and delaying, as well as their direct instantiation for linearizable atomic registers.

Circularity Check

0 steps flagged

No significant circularity; direct proof from asynchronous model

full rationale

The paper proves two general theorems directly from the asynchronous message-passing model (indistinguishability under reordering and delaying of actions) and applies them to linearizable register semantics. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The central claim that extensive message chains are required follows from the model assumptions without reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the standard asynchronous message-passing model in which only send-before-delivery ordering is observable; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Asynchronous message-passing system in which processes observe only that sending a message precedes its delivery
    Explicitly stated as the setting in which ordering information is limited.

pith-pipeline@v0.9.0 · 5484 in / 1087 out tokens · 30500 ms · 2026-05-10T19:35:49.192107+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We start by proving two general theorems that relate message chains to the ability to delay and reorder actions and operations in an execution of an asynchronous system, without the changes being noticeable to the processes. These are then used to prove that linearizable register implementations must create extensive message chains among operations of all types.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Theorem 6 (Delaying the future). Fix a run r of a protocol P, a node θ=⟨i,t⟩, and a delay Δ>0. ... there exists a run r′≈r satisfying ...

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

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